Divergence of $\frac{1}{r^2} \textbf{e}_r$ on $\mathbb{R}^3-0$ is zero?

Question

Divergence of $\frac{1}{r^2} \textbf{e}_r$ on $\mathbb{R}^3-0$ is zero?

Can somebody help me with this calculation? Working in spherical coordinates here. It seems weird to me that this is true, since the flux through any smal parallelpiped would be stronger on the side closer to the origin. Yet this seems to be obvious in the text I'm reading, Arnold's "Mathmatical Methods in Classical Mechanics" chapter 36.

Thanks!